<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><title>R: The Schutz correlation matrix example from Shapiro and ten...</title>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<link rel="stylesheet" type="text/css" href="R.css" />
</head><body>

<table width="100%" summary="page for Schutz"><tr><td>Schutz</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2>
The Schutz correlation matrix example from Shapiro and ten Berge</h2>

<h3>Description</h3>

<p>Shapiro and ten Berge use the Schutz correlation matrix as an example for Minimum Rank Factor Analysis.  The Schutz data set is also a nice example of how normal minres or maximum likelihood will lead to a Heywood case, but minrank factoring will  not. 
</p>


<h3>Usage</h3>

<pre>data("Schutz")</pre>


<h3>Format</h3>

<p>The format is:
num [1:9, 1:9] 1 0.8 0.28 0.29 0.41 0.38 0.44 0.4 0.41 0.8 ...
- attr(*, &quot;dimnames&quot;)=List of 2
..$ :1] &quot;Word meaning&quot;   &quot;Odd Words&quot;    &quot;Boots&quot;      &quot;Hatchets&quot;   ...
..$ : chr [1:9] &quot;V1&quot; &quot;V2&quot; &quot;V3&quot; &quot;V4&quot; ...
</p>


<h3>Details</h3>

<p>These are 9 cognitive variables of importance mainly because they are used as an example by  Shapiro and ten Berge for their paper on Minimum Rank Factor Analysis. 
</p>
<p>The solution from the <code>fa</code> function with the fm='minrank'  option is very close (but not exactly equal) to their solution. 
</p>
<p>This example is used to show problems with different methods of factoring. Of the various factoring methods, fm = &quot;minres&quot;, &quot;uls&quot;, or &quot;mle&quot; produce a Heywood case.  Minrank, alpha, and pa do not. 
</p>
<p>See the blant data set for another example of differences across methods.
</p>


<h3>Source</h3>

<p>Richard E. Schutz,(1958) Factorial Validity of the Holzinger-Crowdeer Uni-factor tests.  Educational and Psychological Measurement, 48, 873-875.
</p>


<h3>References</h3>

<p>Alexander Shapiro and Jos M.F. ten Berge (2002) Statistical inference of minimum rank factor analysis. Psychometrika, 67. 70-94
</p>


<h3>Examples</h3>

<pre>
data(Schutz)
corPlot(Schutz,numbers=TRUE,upper=FALSE)
#f4min &lt;- fa(Schutz,4,fm="minrank")  #for an example of minimum rank factor Analysis
#compare to
#f4 &lt;- fa(Schutz,4,fm="mle")  #for the maximum likelihood solution which has a Heywood case 
</pre>


</body></html>
